a new book in Contact Mechanics... for beginners!

Contact mechanics iswell served by excellent books. Johnson’s Contact Mechanics [1] remains the reference of the field; Barber’s Contact Mechanics [2], Popov’s Contact Mechanics and Friction [3], and Hills, Nowell and Sackfield’s Mechanics of Elastic Contacts [4] cover the subject with rigor and depth. These books were written mainly for graduate students, researchers and specialists. They assume a confident command of elasticity theory, complex variables, integral equations and special functions, and an undergraduate student who opens them for the first time often finds the mathematics, rather than the physics, to be the main obstacle.
This book is meant to fill that gap. It is written for engineering students at the undergraduate level, typically in the second or third year of a Bachelor’s degree, who have taken a first course in mechanics of solids and calculus, but not yet advanced elasticity. The mathematics has been
kept deliberately to an elementary minimum: superposition of simple solutions, dimensional
arguments, energy balances and a few closed-form results that can be checked by hand. Where a full derivation would require tools beyond this level, we state the result, explain where it comes from and show how to use it, rather than prove it. In exchange, we try to explain clearly
why contacts behave as they do, and how simple estimates can be trusted, or not.
Three ideas recur throughout the book: superposition, the analogy between the edge of a contact and the tip of a crack, and the joining of two known limits by the simplest consistent formula. With these, the reader can go from Hertzian contact to partial slip, rough surfaces,
adhesion, viscoelasticity, friction, fretting, rolling, wear and friction-induced vibrations without losing the thread. Each chapter includes short boxes stating the physical idea, worked examples with realistic numbers, and figures computed from the equations in the text; a formula sheet and a table of typical material data are collected in the appendices.
Because the mathematical prerequisites are modest, we hope the book will also reach a wider audience than the existing texts: students of mechanical, civil, materials and biomedical engineering, physicists and engineers in industry who need to estimate a contact pressure, a
friction force or a fatigue risk, and anyone who wishes to approach the specialist literature with a sound physical picture first. Readers who want to go further will find in the books cited above the rigorous developments that are only sketched here.
This text grew out of lecture notes for courses taught at the Politecnico di Bari. We are grateful to the students whose questions shaped it, and we will welcome comments and
corrections from readers.
Bari, October 14, 2026 M. Ciavarella, A. Papangelo, R. Leonetti